Problem 43 - Chemistry and Chemical Reactivity

Question

The simple valence bond picture of \(\mathrm{O}_{2}\) does not agree with the molecular orbital view. Compare these two theories with regard to the peroxide ion, \(\mathrm{O}_{2}^{2-}\) (a) Draw an electron dot structure for \(\mathrm{O}_{2}^{2-} .\) What is the bond order of the ion? (b) Write the molecular orbital electron configuration for \(\mathrm{O}_{2}^{2-} .\) What is the bond order based on this approach? (c) Do the two theories of bonding lead to the same magnetic character and bond order for \(\mathrm{O}_{2}^{2-} ?\)

Step-by-Step Solution

Answer

Valence bond theory gives bond order 1; molecular orbital theory gives bond order 2 and predicts \( \mathrm{O}_{2}^{2-} \) is diamagnetic.

Step 1: Draw Electron Dot Structure

To draw the electron dot structure for \( \mathrm{O}_{2}^{2-} \), we first calculate the total number of valence electrons. Each oxygen atom has 6 valence electrons, and the ion has an extra 2 electrons due to its charge, totaling \( 6 + 6 + 2 = 14 \) electrons. Distribute these 14 electrons to form the most stable structure: place 2 electrons between the oxygen atoms to form a bond and distribute 12 electrons around the oxygen atoms as lone pairs. Each oxygen atom ends up with 3 lone pairs and shares 1 pair for the bond.

Step 2: Calculate Bond Order from Valence Bond Theory

In the valence bond theory, the bond order is calculated based on Lewis structure. For \( \mathrm{O}_{2}^{2-} \), there is only one bond shared between the two oxygen atoms, giving a bond order of 1.

Step 3: Write Molecular Orbital Electron Configuration

For the molecular orbital approach, we consider the molecular orbitals filled with the 14 electrons. The order of filling is: \( \sigma_{2s}^2 \sigma_{2s}^{* 2} \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^{* 2} \pi_{2p_y}^{* 2} \). The molecular orbital electron configuration for \( \mathrm{O}_{2}^{2-} \) is \( \sigma_{2s}^2 \sigma_{2s}^{* 2} \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \).

Step 4: Calculate Bond Order from Molecular Orbital Theory

The bond order in molecular orbital theory is calculated as \( \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \). For \( \mathrm{O}_{2}^{2-} \), the number of bonding electrons is 10 \(( \sigma_{2s}^2, \sigma_{2p_z}^2, \pi_{2p_x}^2, \pi_{2p_y}^2)\) and antibonding electrons is 6 \( (\sigma_{2s}^{* 2}, \pi_{2p_x}^{* 2}, \pi_{2p_y}^{* 2}) \), leading to a bond order of \( \frac{1}{2} (10 - 6) = 2 \).

Step 5: Compare Bonding Theories

The valence bond theory suggests a bond order of 1, while the molecular orbital theory predicts a bond order of 2. The magnetic character differs as well: in molecular orbital theory, \( \mathrm{O}_{2}^{2-} \) is diamagnetic since all electrons are paired, while valence bond theory does not adequately describe magnetic properties without further context.

Key Concepts

Valence Bond Theory

Valence bond theory (VBT) is a foundational concept in understanding chemical bonds. It explains how atoms share electrons in order to form molecules. According to VBT, bonds are formed when atomic orbitals on different atoms overlap and electrons are paired between them.
In the case of the peroxide ion \( \mathrm{O}_{2}^{2-} \), the valence bond model focuses on electron sharing. Here's how it applies:

• Each oxygen atom has 6 valence electrons and with the 2 extra electrons due to the ion’s charge, there are a total of 14 electrons.
• The electrons are arranged around the atoms with one pair between oxygen atoms forming a single bond, leaving each oxygen atom with three lone pairs.
• Based on this Lewis structure, the bond order is calculated by counting shared electron pairs, resulting in a bond order of 1 for the peroxide ion.

The simplicity of VBT sometimes limits its ability to account for more complex phenomena such as magnetic properties and hybridization states.

Electron Configuration

Understanding electron configuration is essential for predicting how electrons are distributed among different orbitals in an atom or molecule. In the molecular orbital (MO) theory, electrons are accommodated in the molecular orbitals, which are formed by the combination of atomic orbitals.
For the peroxide ion, \( \mathrm{O}_{2}^{2-} \), we follow a specific sequence to fill these molecular orbitals:

• The atomic orbitals are combined to form bonding and antibonding molecular orbitals.
• Molecular bonds fill in the order of increasing energy: \( \sigma_{2s}^2 \) \( \sigma_{2s}^{* 2} \) \( \sigma_{2p_z}^2 \) \( \pi_{2p_x}^2 \) \( \pi_{2p_y}^2 \).
• All bonding and antibonding orbitals are carefully considered to determine the placement of the 14 electrons from \( \mathrm{O}_{2}^{2-} \).
Fill the bonding orbitals first, followed by the antibonding ones. This electron filling order provides the electronic configuration of the ion and helps to compare different bonding theories.

Bond Order

Bond order is a crucial concept that provides insight into the stability and strength of a bond. It is determined differently in valence bond and molecular orbital theories, leading to different interpretations.
In valence bond theory for \( \mathrm{O}_{2}^{2-} \):

• The bond order is 1, calculated from the single bond indicated in the Lewis structure.

However, in molecular orbital theory:

• The bond order is calculated using the formula: \( \text{Bond Order} = \frac{1}{2} (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \).
• For \( \mathrm{O}_{2}^{2-} \), there are 10 bonding electrons and 6 antibonding, thus bond order is calculated as \( \frac{1}{2} (10 - 6) = 2 \).

Thus, the molecular orbital theory predicts a stronger bond than the valence bond theory. Understanding these differences highlights the role of bond order in chemical bonding analysis.

Magnetic Properties

Magnetic properties can reveal a lot about the electronic structure of a molecule. Different theories of bonding offer varying insights into these properties.
In the case of the peroxide ion, \( \mathrm{O}_{2}^{2-} \), the molecular orbital theory is particularly helpful:

• Molecular orbital theory indicates that \( \mathrm{O}_{2}^{2-} \) is diamagnetic.
• This is because all the electrons are paired in the molecular orbitals.

In contrast, the valence bond theory, without additional context or modifications such as hybridization and resonance, does not directly accommodate explanations regarding magnetic properties.
Thus, molecular orbital theory provides more comprehensive insights into the diamagnetic nature of \( \mathrm{O}_{2}^{2-} \), demonstrating how unpaired or paired electrons contribute to magnetic behavior.